The Measurement of Inequality of Opportunity

approach yields systematically lower (overall) opportunity shares of inequality, ranging from 17% in Colombia to 34% in Brazil. This is true in all countries, although the difference between θrN and θrP is only approximately 3% (and statistically insignificant) in the case of Brazil. The differences are larger, but either borderline significant or insignificant at the 5% level, in Colombia, Ecuador, Guatemala, and Peru. The country ranking is identical for the two estimation procedures.

These systematic differences are consistent with the expectation (discussed in Section 3) that the large sampling variance within cells with very few observations may cause an upward bias in the non-parametric estimates. Although it can not be ruled out that the (linear) functional form assumption implicit in the parametric estimate might lead to underestimates, the fact that in the only country for which we have a substantially larger sample size (Brazil) the difference almost vanishes provides some support for the suspicion that the bias might come from the sampling variance in small cells in the nonparametric estimates. Nevertheless, given the remaining uncertainty, we make two recommendations: (i) wherever possible, surveys that may be used for measuring inequality of opportunity should collect larger sample sizes; and (ii) where that is not possible, both parametric and non-parametric estimates should be reported to provide a plausible range for the true lower-bound value of inequality of opportunity.

Regarding the effect of each individual circumstance, ΘrJ is highest for family background variables in all countries. This is particularly true for mother’s education which is associated with between 9% and 12% of total inequality. The relative shares of inequalities associated with ethnicity and place of birth vary across countries, with ethnicity being more important in Brazil, Guatemala, and Panama – where it accounts for between 3% and 7% of inequalities – and the geography of birth having more effect in Peru, Brazil and Panama, where it accounts for 4-6% of overall inequality. Finally, inequality of opportunity related to gender ranges from a low of 0-1% in Panama and Colombia, to a high of 5% in Guatemala. In Brazil and Ecuador, gender accounts for 3- 4% of overall inequality.

earlier, labor market participation is almost 100% for men in this age group, but much lower for women. As implied by the reduced-form specification, we are estimating inequality of earnings opportunities conditional on being active in the labor market, so it would be inappropriate to correct for selection.

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household head is endogenous (and thus not a circumstance).33 We therefore work with five circumstances (race, father’s and mother’s education, father’s occupation, and birth place). Income results are reported for all six countries, but consumption data was not available in the PNAD data (for Brazil). Table 8 contains estimates of inequality of opportunity for consumption for Colombia, Ecuador, Guatemala, Panama, and Peru. Tables 9 and 10 report the OLS coefficients of the reduced-form equation (7), for income and consumption expenditures respectively (analogously to Table 6).34

In our samples, overall household income inequality is higher than earnings inequality in Brazil and Panama (by all measures) and in Colombia (by E(1) and E(2), but not by E(0)). It is lower than earnings inequality in Ecuador, Guatemala, and Peru (by all measures), and in Colombia by E(0). In all five countries for which consumption data is available, consumption inequality is considerably lower than either income or earnings inequality. This is consistent with the widespread view that income (and earnings, when these include agricultural and informal sector earnings) is measured with greater error than consumption expenditures, as well as with the expectation that consumption is likely to be closer than current income to permanent income (provided households have access to some consumption-smoothing mechanisms).35

Focusing once again on the path-independent measure E(0), non-parametric estimates of inequality of opportunity for household incomes range from 25% (in Colombia) to 37% (in Guatemala). As for earnings, the parametric estimates are slightly lower: from 23% in Colombia to 35% in Guatemala. For both estimation procedures, the indices are higher than the corresponding estimates for earnings in all countries except for Brazil, where the difference is quite small: 34% for earnings versus 32% for income per capita (for the parametric estimates). In addition to earnings capacity, pre-determined circumstances affect another three important household income determinants: other incomes (such as capital incomes or transfers); the choice of one’s partner; and the composition of the rest of the household (including, most importantly, the number of

33Endogeneity arises both because in some countries reported headship is an interviewee choice, and because household formation (e.g. whether or not one marries) is endogenous.

34All coefficients in these reduced-form regressions have the expected signs, and most are significant at the 1% level. Coefficient sizes are consistent with a reduced-form specification.

35See, e.g. Deaton, 1997, on both of these reasons to prefer consumption to income data in assessing the distribution of welfare in developing countries.

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children). The pattern found in the data suggests that inequality of opportunities in these three domains tends to reinforce the inequality of opportunities that operates through the earnings channel in Colombia, Ecuador, Guatemala, Panama and Peru; but to partially offset them in Brazil.

While total inequality is lower in the distribution of consumption expenditures than in the income distribution, the opposite is true for estimates of inequality of opportunity. The (E(0)) opportunity shares of inequality reported in Table 8 are considerably higher than those reported in Table 7 for all five countries, and regardless of whether the estimates are parametric or non-parametric. The differences are in the 2030% range for Ecuador, Panama and Peru, 40% for Guatemala, but only 6% for Colombia. This supports the notion that income-based measures of inequality of opportunity tend to underestimate lifetime (or permanent income) inequality of opportunity, since transitory income variance (and likely higher measurement error) is effectively counted as inequality due to “efforts and luck”.36 Our non-parametric (parametric) estimates of inequality of opportunity in the distribution of consumption expenditures are: 27% (24%) in Colombia, 34% (32%) in Ecuador, 35% (34%) in Peru, 42% (39%) in Panama, and 52% (50%) in Guatemala.37

Figure 3 graphically depicts the decomposition of household consumption inequality into the lower-bound inequality of opportunity and a residual term, associated with effort differences and luck, for both the parametric and the (path-independent) nonparametric method. Despite the sample size limitations (especially for Panama and Guatemala), the parametric and non-parametric estimates turn out to be very close. These differences are smaller for consumption inequality than for earnings, reflecting larger sample sizes, and thus a lower proportion of cells with zero or few observations (see Table 4). Although the parametric estimates remain systematically below their nonparametric counterparts, the differences are now never statistically significant, and the country ranking is identical.

36See Bourguignon et al. (2007) for a discussion. The finding is analogous to the well-known fact that inter-generational mobility estimates are much higher when based on single-period wages for parents and children, than when based on longer earnings histories. See, inter alia, Solon (1999) and Mazumder (2005).

37With the exception of the difference between Ecuador and Peru, all cross country differences are significant at the 5% level, on the basis of the bootstrapped standard errors.

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Figure 3 also provides an intuitive illustration of the distinction between the absolute-Θ measures of inequality of opportunity (defined in equation 4) and the relative- Θ measures (defined in equation 5). The level of E(0) corresponding to (either the parametric or the non-parametric) estimate of inequality of opportunity (the lower part of the bar in Figure 3) is an example of the absolute measures θ : {yik }→ + ,

θ({yik })= IB({yik }). The ratio of this lower segment to the height of the entire bar yields an

Turning to the analysis of individual circumstance variables, we find that family background characteristics are once again associated with the largest share of inequality of opportunity. The share of inequality accounted for by mother’s education alone is higher than 15% in most countries, and as high as 26% in Guatemala. The share of inequality associated with the other variables is usually higher than for earnings, with the same broad ranking across different circumstances (parental background more important than either race or birth region). The higher levels of inequality of opportunity observed in Central American countries, however, are associated with larger partial shares for region of birth (which is also important in Peru) and ethnicity.

7. The Opportunity-deprivation Profile: Identifying the Least Advantaged

Groups

The analysis has so far focused on scalar measures of inequality of opportunity in each country, largely expressed as shares of total outcome inequality. These indices can be useful to summarize the importance of a set of predetermined circumstances in the structure of inequality in a particular country. Since the relative measures are not closely correlated with measures of outcome inequality, they are also informative of some of the differences in the nature of inequality across countries. Ultimately, a country where a smaller share of total inequality is associated with differences in opportunity is likely to be a fairer society, where individual choices and effort (and luck) play a greater role in determining outcomes than family origin, race or gender.

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However, the partition of the population {yik }into K types, which is undertaken to generate these indices, can also be used to yield a byproduct of potentially even greater interest to analysts and policymakers alike. Recall that each cell in the partition

have seen that equal opportunities attain when Fk (y)= Fl (y), k ≠ l , which is a different way of writing F(y C)= F(y) for a discrete partition. Differences in the outcome

distributions among types therefore are taken to reveal (or arise from) inequality of opportunity.

At least conceptually, it is not unreasonable to see Fk (y) as an individual i’s ( i k ) opportunity set for outcome y. Given i’s circumstances Cik , only i’s own choices, efforts and luck will determine his final position, pi = Fk (yi ). If it were possible, therefore, to rank Fk (y) across k in a meaningful way, we would obtain a ranking of opportunity sets across types, which we call an opportunity profile.

As previously discussed, one obvious such ranking would be given by any (firstor second-order) stochastic dominance relationships between types. However, the stochastic dominance approach to constructing an opportunity profile suffers from two problems. The first, which is conceptual in nature, is that any such ranking is perforce partial and incomplete (see Atkinson, 1970). The second, which is practical in nature, is that the distribution of cell sizes partly summarized in Table 4 makes it impossible to estimate the conditional distributions for the full set of 54 – 216 types in our partitions.

Albeit conceptually less satisfactory, a feasible alternative ranking algorithm would be to use a particular moment of Fk (y), such as the mean, or indeed a particular percentile, such as the median, the first quartile, etc. Because the type’s mean outcome,

μk , was central in constructing smoothed and standardized distributions, and thus for the decomposition exercises reported in Sections 5 and 6, we choose to use it as the ranking criterion for the type-specific opportunity sets Fk (y) in what follows. While this strikes us as a reasonable choice, it is still arbitrary, and the reader is cautioned that alternative criteria are certainly possible, and might imply different rankings.

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Furthermore, we choose to focus only on the least-advantaged types in a society – those with the lowest-ranking opportunity sets. We avoid the issue of setting an “opportunity deprivation threshold”, and choose simply to consider the types that account for the bottom 10% of the population. In other words, we rank all types in each country in increasing order of mean outcome. The bottom m groups are included in that country’s opportunity profile, where the population share over m sums to 10%. Formally, these are

{k k (1,..., m)}as the opportunity-deprivation profile; and to the individuals i that belong

to those types as the opportunity-deprived.

Table A1 in the appendix lists the full opportunity-deprivation profiles for each of our six countries, described by the specific circumstances that define them (ethnicity, mother’s and father’s education levels, father’s occupation and birthplace). It also reports their population sizes and shares, as well as their mean per capita consumption (in levels and as shares of the national means).38 The number of types in the opportunitydeprivation profile varies across countries: There are 5 such groups in Guatemala and Peru, 6 in Brazil, 10 in Colombia, 16 in Ecuador, 20 in Mexico, and 25 in Panama. Some types represent large populations (there are two groups in the Brazilian profile that represent more than 2 million people each) while others represent only a few hundred individuals.

When presented in their “full” form, as in Table A1, opportunity-deprivation profiles are simply a list of the types with the lowest-ranking opportunity sets in each country in our sample. For comparative purposes, however, it may be useful to have a synthetic overview of the opportunity-deprived group as a whole, in each country. Table 11 thus summarizes a number of characteristics of all opportunity-deprived individuals in our six countries. Three common traits are salient. First, members of ethnic minorities form the vast majority of the population in these disadvantaged groups. In three of our six countries, these groups are composed exclusively of members of racial or ethnic

38 It is of course possible to construct similar profiles for each of our three concepts of economic advantage, but we report one only for household consumption per capita. Per capita income is used for Brazil.

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minorities: black and mixed-race in Brazil; and native speakers of indigenous languages in Guatemala and Peru. In two other countries, ethnic minorities are still a majority of the opportunity-deprived: 76% of the opportunity profile in Panama consists of native speakers of indigenous languages; and 61% of self-reported indigenous, black or mixedrace ethnicity in Ecuador. Colombia is the only country in our sample where ethnic minorities are not the majority among the opportunity-deprived but, even there, the proportion of minorities, 33%, is still higher than in the population as a whole.

Second, family background is also strongly associated with opportunitydeprivation. In the four countries where this information is available, never fewer than 83% of the opportunity-deprived are daughters and sons of agricultural workers, and this proportion reaches 100% in Guatemala. Almost the same holds for parental education: In all countries, more than 90% of the opportunity-deprived are daughters and sons of women who did not go to school – 99% in Guatemala and Peru, 98% in Ecuador, 96% in Colombia, 93% in Panama, and 91% in Brazil. Similar results hold for father’s education, although in Colombia, Ecuador and Panama, father’s education is a less powerful predictor of opportunity deprivation than mother’s education.

Third, opportunity deprivation is remarkably spatially concentrated. A majority of the opportunity-deprived are often natives of the same specific regions. In Brazil, all persons in our profile were born in the Northeast or North regions; in Colombia, 99% hail from peripheral departments; in Guatemala, 99% come from one of the North and Northwestern departments; in Panama, 96% were born in a rural area.39 There is somewhat greater spatial heterogeneity in the opportunity-deprivation profiles for Ecuador and Peru.

Does opportunity deprivation manifest itself in lower economic achievement levels? Qualitatively the answer is “yes” by construction, since the types were ranked by mean economic achievement. Quantitatively, the last row in Table 11 gives the income share of the opportunity deprived in each country. Since they account for 10% of the population in all countries by construction, the distance between their income (or consumption expenditure) share and 10% can be seen as a rough quantitative measure of the economic consequences of opportunity deprivation in each country. The income share

39 Geographical regions are not reported in the survey for Panama, so an urban-rural subdivision was used instead.

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of the 10% of the population we classify as opportunity deprived is 2,7% in Panama, 2.9% in Brazil, 3.5% in Guatemala, and 4.4% in Ecuador, 4.8% Peru, and 5.0% in Colombia.40

We conclude this section with a brief discussion of the differences between the opportunity-deprivation profile we have introduced, and the more standard concept of a poverty profile. A poverty profile describes the characteristics of individuals with individual incomes below a poverty line, whereas the opportunity profile ranks individuals by the mean income (or consumption) of the type they belong to. These are conceptually very different objects. An opportunity-deprivation profile will include individuals from very disadvantaged backgrounds, who happened to be successful and have escaped poverty through their own efforts or sheer luck. A poverty profile will not. An opportunity-deprivation profile will exclude individuals from more advantaged backgrounds, who did poorly either through bad luck or poor performance, whereas a poverty profile will include them.

Differences between the two profiles may, therefore, contain information on how powerful circumstances are in determining poverty outcomes. If there is very little difference, effort and luck would appear to be largely powerless to compensate for the initial opportunity deprivation individuals inherit. Conversely, if there is limited overlap between the two profiles, one could claim that initial circumstances matter little to a person’s chances of escaping poverty. Table 12 describes the poverty profile for our six countries, by arbitrarily fixing the poverty line at the first decile in each distribution. In this fashion both profiles refer to the “bottom” 10% of the population, with the difference arising from the ranking criterion used to define “bottom”.

The comparison of the two profiles reveals interesting patterns. Unsurprisingly, the opportunity-deprived are more homogenous than the poor with respect to most circumstance variables. Although ethnic minorities form the majority of the opportunitydeprived in five countries (and 100% in Brazil, Guatemala and Peru) they account for lower shares of the poor: 70% in Guatemala, 69% in Brazil, 56% in Peru, 54% in

40 One can also isolate the types that account for the top end of the opportunity profile in each country. Call them “opportunity hoarders”. Their income shares are 22.6% in Panama, 23.1% in Ecuador, 23.7% in Peru, 25.8% in Colombia, 28.8% in Brazil, and 29.3% in Guatemala. Details of the “opportunity-hoarding” profile for our six countries is available from the authors on request.

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Panama, 32% in Ecuador, and 15% in Colombia. A similar pattern arises for place of birth: poverty is less spatially concentrated than economic opportunity: 70% of the poor in Brazil live in the North or Northeast (as compared with 100% of the opportunitydeprived being born there). 65% of the poor live in Colombia’s peripheral departments, while 99% of the opportunity-deprived were born there. And so on. Family backgrounds are also more heterogeneous among the poor than among the opportunity deprived, although the share of children of agricultural workers is still very high at 80% in Ecuador and Panama, and 75% in Guatemala.

The last row in Table 12, analogously to Table 11, provides the income share of the poor in each country. They are 0.7% in Brazil (using income per capita), 1.5% in Colombia and Panama, 1.8% in Guatemala and Peru, and 1.9% in Ecuador. The ratio of the income share of the opportunity-deprived to the income share of the poor is 1.80 in Panama; 1.94 in Guatemala; 2.31 in Ecuador; 2.66 in Peru, 3.33; in Colombia; and 4.14 in Brazil.41 Since the income share of the opportunity-deprived is larger when some among them succeed in escaping poverty, these ratios are suggestive indicators of “mobility”. The higher the ratio, the less opportunity-deprivation would seem to amount to a sentence of life in poverty, delivered at birth. Nevertheless, more confident statements on the relationship between opportunity-deprivation profiles, poverty profiles, and more standard measures of mobility (which largely rely on the association between outcomes and one particular circumstance, such as father’s wage or education), would require further work.42

8.Conclusions

This paper has proposed a simple conceptual framework for the measurement of inequality of opportunity, which derives two empirical tools directly from John Roemer’s theory of equal opportunities. The first tool is a class of scalar indices that measure

41The number for Brazil is not comparable to those of the other countries, since it is built on an income, rather than consumption expenditure, distribution.

42Van de Gaer et al. (2001) contain a pioneering theoretical discussion of the relationship between mobility and equality of opportunity. See also Gaviria (2007) for a recent survey of intergenerational mobility in Latin America, with some discussion of attitudes to redistribution. Fields et al. (2007) provide a survey of the evidence on intra-generational income mobility in the region.

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